Well, I'm not sure about this. (I'm always too lawful or avoid getting caught in the first place)
Anyway, today I just happened to be wandering about the market district when I overheard a rumour about the Imperial Watch being corrupt. I then got a message about a new topic which was about this corruption, which suggests I've stumbled upon a quest.
Now I haven't followed up on the quest but here is a possible explanation. If the watch is corrupt as the rumour goes (and rumours are pretty much always right in games.), then the nonlocked chest might be a symptom. Imagine the following exchange.
"Stop, criminal. It's off to jail with you.

"
"Is that really necessary? If you would just let me walk, I could make it worth your while.

"
"Deal. Now I'm going to take you to the prison so we can get the forms filled out. All stolen items will be confiscated. Now here is what is not going to happen. You will not hear from me that we will place your items in a chest that is easy to get to.

I will also refuse to tell you that this chest is the one chest that does not have a lock.

Now follow me, criminal."
So yeah, maybe there is no lock on the chest because the guards are basically turning a blind eye to all the criminals who want to recover their loot.
The other possible reason I can come up with is the more likely one but rather stupid. Bethesda forgot to put a lock on it.